Powerful FE approaches for Pochhammerʹs dispersion modelling

Simple and very e ective nite element approaches for modelling of the dispersion of torsional, longitudinal and exural waves propagated in in nite and elastic cylindrical bars (Pochhammer’s problem) and hollow cylinders are presented. The approaches allow to model given problems without using in nite elements and their usage is demonstrated by using dispersion curves, shapes of waves and tables of phase velocities. Comparison of nite element solutions (solved in one task from small-sized models) with exact solutions shows an excellent agreement. The maximum relative di erences among the 20 lowest FEM and analytical phase velocities was less than 0.000015%. The approaches and results hold also for cylinders with nite lengths, simply supported on both ends